2) If you want to visualize actual magnetic force, then nthing iron filings. If you want to visualize what magnetic fields are like without actually having any (i.e. the analog of the gravity thing) just do the gravity thing. Then explain that you can also have the balls distort space "up" as well as "down".posted by DU at 2:41 AM on December 29, 2009

The one issue is that the magnetic force acts in two different ways. Dipole magnets (your standard North-South bar magnet) like iron filings will orient themselves along the direction of magnetic fields. This is why they are good for mapping out magnetic field lines. However, magnetic fields also interact with charged particles in a completely different way. They want to do circles around magnetic field lines. This means that they will make loops around field lines, like in this (kinda dull) video. However, it means that if charged particle comes in at the right angle or has a certain energy, they can loop around and follow field lines, like in these illustrations from NASA depicting charged particles from the sun (solar wind) hitting Earth's magnetic field. Earth's magnetic field is a fantastic thing to look at in its own right, created by electrical currents in the Earth's core. I suggest looking at this old Astronomy Picture of the Day.

That's a brief introduction to how things interact with magnetic fields, but I've skipped over how they are generated. Atomic nuclei, due to quantum mechanics, act like little dipole magnets. In permanent magnets, all of these nuclei line up in the same direction, giving you a big dipole magnet. This is what you have on your fridge. However, just as charged particles are moved by magnetic fields, so do they create magnetic fields. A straight wire with a constant current running through it will generate magnetic field lines that form circles around it. More complicated geometries of current will have more complicated magnetic fields, like in the Earth's core image.

The overall story is that magnetic fields are far more complicated than gravity (on some level) in how they are generated and how they interact with particles. I would be surprised if a good unified summary of all of the important parts of magnetic fields exists, but at the same time every little bit should be visualizable.posted by Schismatic at 3:15 AM on December 29, 2009 [3 favorites]

Also, magnetic fields and electric fields are really two aspects of the same force, depending on the relative velocity of the observer and the object generating the field.

I clicked in just to say this. If you see how a magnetic field originates from a moving electric current, maybe you can see how it is no different than what is seen by zooming past a stationary line of charges. This is a fascinating aspect of electromagnetism essential to special relativity, as Schismatic pointed out. No understanding of magnetism is complete without it, especially when you consider the origination of magnetism at the atomic level.

Also, not to confuse you, but the gravity of general relativity isn't as simple as central-force distortions in space time. Moving or spinning objects are thought to create a different kind of space-time stress more akin to a torsion; the effect is called gravitomagnetism in analogy to the magnetic/electric duality only.

Then, of course, it's worth mentioning gravitational waves (radiation). Since there is only one mass charge (compared to positive and negative electric charges), the waves bear only slight resemblance to EM waves; they are quadrupolar rather than dipolar. That means that as they pass, they will pinch an observer in one direction and pull in the orthogonal direction. A polarized EM wave simply shakes a charge in one particular direction.

A word of caution regarding the iron filings. It encourages a mistaken idea that magnetic fields consist of discrete lines, or are structured in onion-like layers, and that the iron filings are lining up along these individual lines. This is not correct, and in the absence of the filings the magnetic field is smooth.posted by edd at 6:31 AM on December 29, 2009

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